Critical Exponents in a Quantum Phase Transition of an Anisotropic 2D Antiferromagnet

I use the two-step density-matrix renormalization group method to extract the critical exponents $\beta$ and $\nu$ in the transition from a N\'eel $Q=(\pi,\pi)$ phase to a magnetically disordered phase with a spin gap. I find that the exponent $\beta$ computed from the magnetic side of the transition is consistent with that of the classical Heisenberg model, but not the exponent $z\nu$ computed from the disordered side. I also show the contrast between integer and half-integer spin cases.Comment: 4 pages, 2 figure

Antiferromagnetism and phase separation in the t-J model at low doping: a variational study

Using Gutzwiller-projected wave functions, I estimate the ground-state energy of the t-J model for several variational states relevant for high-temperature cuprate superconductors. The results indicate antiferromagnetism and phase separation at low doping both in the superconducting state and in the staggered-flux normal state proposed for the vortex cores. While phase separation in the underdoped superconducting state may be relevant for the stripe formation mechanism, the results for the normal state suggest that similar charge inhomogeneities may also appear in vortex cores up to relatively high doping values.Comment: 4 pages, 3 figures, reference adde

Order and Disorder in AKLT Antiferromagnets in Three Dimensions

The models constructed by Affleck, Kennedy, Lieb, and Tasaki describe a family of quantum antiferromagnets on arbitrary lattices, where the local spin S is an integer multiple M of half the lattice coordination number. The equal time quantum correlations in their ground states may be computed as finite temperature correlations of a classical O(3) model on the same lattice, where the temperature is given by T=1/M. In dimensions d=1 and d=2 this mapping implies that all AKLT states are quantum disordered. We consider AKLT states in d=3 where the nature of the AKLT states is now a question of detail depending upon the choice of lattice and spin; for sufficiently large S some form of Neel order is almost inevitable. On the unfrustrated cubic lattice, we find that all AKLT states are ordered while for the unfrustrated diamond lattice the minimal S=2 state is disordered while all other states are ordered. On the frustrated pyrochlore lattice, we find (conservatively) that several states starting with the minimal S=3 state are disordered. The disordered AKLT models we report here are a significant addition to the catalog of magnetic Hamiltonians in d=3 with ground states known to lack order on account of strong quantum fluctuations.Comment: 7 pages, 2 figure

Stacking Faults, Bound States, and Quantum Hall Plateaus in Crystalline Graphite

We analyze the electronic properties of a simple stacking defect in Bernal graphite. We show that a bound state forms, which disperses as |\bfk-\bfK|^3 in the vicinity of either of the two inequivalent zone corners \bfK. In the presence of a strong c-axis magnetic field, this bound state develops a Landau level structure which for low energies behaves as E\nd_n\propto |n B|^{3/2}. We show that buried stacking faults have observable consequences for surface spectroscopy, and we discuss the implications for the three-dimensional quantum Hall effect (3DQHE). We also analyze the Landau level structure and chiral surface states of rhombohedral graphite, and show that, when doped, it should exhibit multiple 3DQHE plateaus at modest fields.Comment: 19 page

Spin 3/2 dimer model

We present a parent Hamiltonian for weakly dimerized valence bond solid states for arbitrary half-integral S. While the model reduces for S=1/2 to the Majumdar-Ghosh Hamiltonian we discuss this model and its properties for S=3/2. Its degenerate ground state is the most popular toy model state for discussing dimerization in spin 3/2 chains. In particular, it describes the impurity induced dimer phase in Cr8Ni as proposed recently. We point out that the explicit construction of the Hamiltonian and its main features apply to arbitrary half-integral spin S.Comment: 5+ pages, 6 figures; to appear in Europhysics Letter

Floquet Spectrum and Transport Through an Irradiated Graphene Ribbon

Graphene subject to a spatially uniform, circularly-polarized electric field supports a Floquet spectrum with properties akin to those of a topological insulator, including non-vanishing Chern numbers associated with bulk bands and current-carrying edge states. Transport properties of this system however are complicated by the non-equilibrium occupations of the Floquet states. We address this by considering transport in a two-terminal ribbon geometry for which the leads have well-defined chemical potentials, with an irradiated central scattering region. We demonstrate the presence of edge states, which for infinite mass boundary conditions may be associated with only one of the two valleys. At low frequencies, the bulk DC conductivity near zero energy is shown to be dominated by a series of states with very narrow anticrossings, leading to super-diffusive behavior. For very long ribbons, a ballistic regime emerges in which edge state transport dominates.Comment: 4.2 pages, 3 figure